How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_5 18?

1 Answer
Oct 31, 2015

${\log}_{5} 18 = \frac{\ln \left(18\right)}{\ln \left(5\right)}$ or ${\log}_{5} 18 = \frac{{\log}_{10} \left(18\right)}{{\log}_{10} \left(5\right)}$

Explanation:

${\log}_{a} b = \frac{{\log}_{c} \left(b\right)}{{\log}_{c} \left(a\right)}$
for all positive real numbers a,b and c.

In this case, $a = 5$, $b = 18$, $c = e$ or $c = 10$